A rope loop of radius \(r = \SI[per-mode=symbol]{0.1}{\meter}\) and mass \(m = 50\pi\,\text{g}\) rotates on a frictionless table such that the tangential velocity of any point on the loop is \(v_\textrm{tangential}=\SI[per-mode=symbol]{6}{\meter\per\second}.\)

33 ants are placed on a pole of length \(\SI{1.0}{\meter}.\) They each have negligible length, and they each crawl with a velocity of \(\SI[per-mode=symbol]{1}{\centi\meter\per\second}.\) If two ants meet head on, they both turn around and immediately continue crawling.

If an ant reaches either end of the pole, the ant will drop off the pole. What is the longest possible time (in seconds) until all the ants drop off the pole?